This puzzle was given to me by a graduate student in a Kant class that I was teaching and I use it to “illustrate” some of Kant’s philosophy. At the center of the puzzle is a glass orb. The orb is surrounded by rods and the rods are held together by a cord. In my version of the philosopher’s knot, the rods are held together by red and purple yarn.
In using this puzzle to explain some of Kant’s philosophy, I ask the students to imagine that we are “inside” the knot, in the position of the orb. We are surrounded by the rods. The rods are analogous to the concepts in Kant's philosophy, so we are, or live, “inside” of our conceptual framework. The rods, however, are bounded by red and purple yarn. Similarly, according to Kant, our concepts must be bounded by the intuitions of space and time.
Compare and contrast this philosopher's knot with the following analogy made by Kant himself. "Our reason is not like a plane indefinitely far extended, the limits of which we know in a general way only; but must rather be compared to a sphere, the radius of which can be determined from the curvature of the arc of its surface - that is to say, from the nature of the synthetic apriori propositions - and whereby we can likewise specify with certainty its volume and its limits. Outside this sphere (the field of experience) there is nothing that can be an object for reason; nay, the very questions in regard to such supposed objects relate only to subjective principles of a complete determination of those relations which can come under the concepts of the understanding and which can be found within the empirical sphere." [Kant, The Critique of Pure Reason, translated by Norman Kemp Smith, A762B790]
While analogies and models can be useful in clarifying relationships that we did not understand, one must also be careful, because an analogy and a model can mislead one. In explaining the analogy between a portion of Kant’s philosophy and the Philosopher’s Knot one problem is the “we”. Is each person “inside” the concepts (which are bounded by space and time) or are we as a community “inside” the concepts?